A Second Glass Transition Observed in Single-Component Homogeneous Liquids Due to Intramolecular Vitrification

Abstract

On supercooling a liquid, the viscosity rises rapidly until at the glass transition it vitrifies into an amorphous solid accompanied by a steep drop in the heat capacity. Therefore, a pure homogeneous liquid is not expected to display more than one glass transition. Here we show that a family of single-component homogeneous molecular liquids, titanium tetraalkoxides, exhibit two calorimetric glass transitions of comparable magnitude, one of which is the conventional glass transition associated with dynamic arrest of the bulk liquid properties, while the other is associated with the freezing out of intramolecular degrees of freedom. Such intramolecular vitrification is likely to be found in molecules in which low-frequency terahertz intramolecular motion is coupled to the surrounding liquid. These results imply that intramolecular barrier-crossing processes, typically associated with chemical reactivity, do not necessarily follow the Arrhenius law but may freeze out at a finite temperature.

Figure 1

Cartoon structures of four transition-metal alkoxides. Only the oxygen atoms of the alkoxide groups are shown here. Silicon alkoxides have the formula Si(OR)₄; silicon prefers tetrahedral coordination and is therefore monomeric in the liquid and crystal. Niobium alkoxides have the formula Nb(OR)₅; niobium prefers octahedral coordination and is therefore dimeric in the liquid and crystal. Titanium alkoxides have the formula Ti(OR)₄, while titanium prefers octahedral coordination. Due to steric hindrance, these typically form trimers in the liquid. If the alkoxide is short (methoxide and ethoxide), it can crystallize in the tetrameric form. Aluminum alkoxides have the formula Al(OR)₃; aluminum prefers octahedral coordination, resulting in trimers in the liquid and tetramers in the crystal.

Figure 2

Calorimetry of titanium-based alkoxides shows two calorimetric glass transitions. Heat capacity measurements of titanium ethoxide, propoxide, butoxide, hexoxide, 2-ethylhexyloxide, and 2-ethylhexanoate as well as niobium butoxide. (a) Data obtained using quench cooling with liquid nitrogen to ∼120 K and heating at 20 K/min. See also Table S1. Curves have been shifted vertically for improved visibility. (b) Data obtained using controlled cooling to ∼190 K and heating at 10 K/min. See also Table S2. (c) The magnitude of the change in heat capacity at the second glass transition, ΔC_p-intra, as a function of the volume fraction of titanium butoxide on mixing with silicon butoxide.

Figure 3

Optical Kerr-effect (OKE) spectra of supercooled and vitrified alkoxide liquids. (a) Data on titanium 2-ethylhexyloxide from 150 to 300 K (solid lines) and fit to a Cole–Cole function representing diffusive modes, a Brownian oscillator (∼1.3 THz) representing alkoxide librations, and a single Brownian oscillator (∼7–8 THz) representing multiple intramolecular vibrational modes. The inset shows the temperature-dependent librational frequency and amplitude of the diffusive mode. (b) Data on niobium ethoxide from 190 to 310 K with similar fits and parameter values in the inset.

Figure 4

Viscosity measurements of titanium butoxide and titanium 2-ethylhexyloxide. Shear viscosity up to a maximum of ca. 10¹⁰ Pa·s (green circles) for titanium butoxide (top) and titanium 2-ethylhexyloxide (bottom). The lines are the fits of two separate Vogel–Fulcher–Tammann (VFT) expressions (blue and red lines, parameters in Table S6). The right axis shows the loss tangent.

Figure 5

Structure and dynamics of the trimeric alkoxides. (a) Molecular models of the titanium cores of trimeric titanium alkoxides. The five clusters shown have similar energies with the lowest-energy isomer dependent on the alkoxide chain length. Only the titanium (gray) and oxygen atoms (red) are shown. (b) Titanium-core bending modes are strongly coupled to the liquid. Normal-mode calculations show that most vibrational modes between ca. 80 and 150 cm^–1 (2.5–5 THz) involve Ti₃-core bending and twisting motions with significant displacement of the terminal carbons of alkoxide side chains causing strong coupling to the surrounding liquid. Shown here is mode 31 (89 cm^–1/3 THz) in isomer IV as a typical example of this effect.